In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero at P, a polynomial in one fixed variable z, which is monic, and whose coefficients of lower degree terms are analytic functions in the remaining variables and zero at P.
There are also a number of variants of the theorem, that extend the idea of factorization in some ring R as u·w, where u is a unit and w is some sort of distinguished Weierstrass polynomial. Carl Siegel has disputed the attribution of the theorem to Weierstrass, saying that it occurred under the current name in some of late nineteenth century Traités d'analyse without justification.
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In mathematics, the Weierstrasspreparationtheorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It...
Several theorems are named after Karl Weierstrass. These include: The Weierstrass approximation theorem, of which one well known generalization is the...
In mathematics, the Malgrange preparationtheorem is an analogue of the Weierstrasspreparationtheorem for smooth functions. It was conjectured by René...
Preparationtheorem may refer to: Malgrange preparationtheoremWeierstrasspreparationtheorem This disambiguation page lists mathematics articles associated...
X} ) is coherent. Cartan's theorems A and B Several complex variables GAGA Oka–Weil theoremWeierstrasspreparationtheorem Noguchi (2019) In Oka (1950)...
prime ideal is a finite extension of a regular local ring. The Weierstrasspreparationtheorem can be used to show that the ring of convergent power series...
series with coefficients in a complete local ring satisfies the Weierstrasspreparationtheorem. Formal power series can be used to solve recurrences occurring...
particular a unique factorization domain. It follows from the Weierstrasspreparationtheorem for formal power series over a complete local ring that the...
intermediate value theorem (also known as Bolzano's theorem). Today he is mostly remembered for the Bolzano–Weierstrasstheorem, which Karl Weierstrass developed...
mathematicians Niels Henrik Abel and Évariste Galois in algebra. Sylow theorems and p-groups, known as Sylow subgroups, are fundamental in finite groups...
mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after...
functions, factorization theorem, function, M-test, preparationtheorem – Karl Theodor Wilhelm Weierstrass Wien bridge – Max Wien Weissenberg effect – Karl...
to Berlin, Gibbs attended the lectures taught by mathematicians Karl Weierstrass and Leopold Kronecker, as well as by chemist Heinrich Gustav Magnus....
analytical theory; they also began the use of hypercomplex numbers. Karl Weierstrass and others carried out the arithmetization of analysis for functions...
history of medicine at Fordham University; Laetare Medal recipient Karl Weierstrass (1815–1897) – often called the father of modern analysis Anna Wierzbicka...
functionum ellipticarum with his elliptic theta functions. By 1841, Karl Weierstrass, the "father of modern analysis", elaborated on the concept of absolute...
infinitesimals in mathematics was frowned upon by followers of Karl Weierstrass, but survived in science and engineering, and even in rigorous mathematics...
1863–1883". Science and Society Picture Library. Retrieved 2009-02-05. "Weierstrass summary". University of St Andrews. Retrieved 2009-02-03. "Rayleigh summary"...
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